Modelling flow and heat transfer in fractured rocks: dimensional effect of matrix heat diffusion Original Research Article

This work examines heat transfer in fractured crystalline rocks with application to heat mining from hot dry rocks (HDR). The object of this study is to investigate the dimensional effect of heat diffusion within the rock matrix. Analytical models based on the Laplace-transform technique assume one-dimensional heat flow within the rock matrix perpendicular to the fracture plane. These so called image models result from 2-D heat transfer within fractures and 1-D heat transfer within the adjacent rocks. Numerical methods allow fully 3-D modelling which reflects the natural situation of spatial heat propagation in rock formations. The numerical model is verified against analytical solutions at the image level. Valid discretisations are obtained with respect to the strong heterogeneity of the fractured medium. The dimensional effect of matrix-heat-diffusion is quantified by comparison of conventional image with 3-D models. In the example considered the reduced dimension models overestimate the thermal drawdown by up to 11 % after 20 years of production. This fact indicates the importance of 3-D modelling. Finally, the new model is applied to the prediction of minimum borehole separations for a European HDR prototype system at Soultz-sous-Forets, Alsace, France.